1. Seminar on
MICHAELIS MENTEN
KINETICS
PRESENTED BY
MOHAMMED MUNAWAR ALI
(M.PHARM. 1 ST SEMESTER)
DEPT. OF PHARMACEUTICS
ST. PETER’S INSTITUTE OF
PHARMACEUTICAL SCIENCES,
VIDYANAGAR, HANAMKONDA. 506001.
AFFILIATED TO KAKATIYA UNIVERSITY
2. C ONTENTS
Introduction
Some pharmacokinetic aspects of Michaelis-Menten equation.
In vivo estimation of Km and Vm
Estimation of pharmacokinetic parameters concerned
Other Non-linear Processes
Problems in quantifying non-linear kinetics
Conclusion
References
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3. I NTRODUCTION
Linear kinetics, wherein the change in plasma
concentration of drug due to absorption, distribution,
binding, metabolism or excretion is proportional to its
dose whether administered as single or multiple doses.
Drug biotransformation, renal tubular secretion, and
biliary secretion usually require enzyme or carrier
systems. These systems are relatively specific with
respect to substrate and have finite capacities, such
processes are called capacity limited process; commonly
called non-linear pharmacokinetics.
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4. The pharmacokinetics of such drugs which follow non-
linear are said to be dose dependent, mixed order or
capacity limited process.
The kinetics of capacity limited process are best
explained by Michaelis-Menten equation, given as
This equation is derived from the following scheme.
E = conc. of enzyme
K-1 K C = conc. of drug
E+C K1
EC 2
E+M EC= conc. of enzyme-drug complex
M = conc. of metabolite
K2 and K-1 = first order rate constants
K1 = second order rate constant 4
5. Table-1
Causes of non linearity Examples
Absorption
Saturable transport in gut wall Riboflavin
Drug comparatively insoluble Griseofulvin
Saturablegut wall or hepatic metabolism on first pass Salicylamide, propranolol
Pharmacologic effect on GI motility Metoclopramide, chloroquine
Saturable gastric or GI decomposition Some penicillins
Distribution
Saturable plasma protein binding Phenylbutazone, salicylates
Saturable tissue binding Naproxen
Saturable transport into or out of tissues methotrexate
Renal elimination
Active secretion Penicillin G
Active reabsorption Ascorbic acid
Change in urine pH Salicylic acid
Saturable plasma protein binding Salicylic acid
Nephrotoxic effect at higher doses Amino glycosides
Diuretic effect Theophylline, alcohol
Extra renal elimination
Capacity limited metabolism Phenytoin, theophylline
Enzyme saturation or co-factor limitation Salicylic acid, alcohol
Saturable biliary secretion Tetracycline, indomethacin
Enzyme induction Carbamazepine
Hepatotoxic at higher doses Acetaminophen
Saturable plasmaproteinbinding Phenylbutazone
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Altered hepatic blood flow Propranolol
Metabolite inhibition. Diazepam
6. SOME PHARMACOKINETIC
ASPECTS
Three conditions are considered here where the
michaelis-menten equation alter depending.
i) when Km=C
-dC/dt= Vm/2
ii) when Km>>> C
-dC/dt= (Vm/Km)C
iii) when Km<<< C
-dC/dt= Vm Fig 1
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Source: Milo Gibaldi, Pharmacokinetics
7. In vivo ESTIMATION OF K m AND V m
When drug is administered via IV injection, eliminated by single capacity
limited process.
Solving the equation we get,
Modified form of which is,
Conversion to common logarithmic form
and solving for log C,
Fig 2.
Source: Milo Gibaldi, Pharamacokinetics
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9. Considering the drug elimination involving one capacity limited process and
one or more first order processes, the rate of elimination is represented as,
Km<<<C
Km>>>C Plot -d ln C/dt Vs 1/C
where slope is Vm. To get
Km the eq. is considered at
lower concentration.
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11. USAGE OF URINE DATA
K’
V’m kmu
K’m
V’m is maximum rate of metabolite,
K’ & kmu are first order rate constants,
K’m is michaelis-menten’s constant,
Cm is plasma drug conc. at midpoint of
collection interval.
Fig 5. 11
Source: Milo Gibaldi, Pharamacokinetics
13. For the case where linear pathways of elimination in parallel with a
non-linear process,
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14. OTHER NON-LINEAR PROCESSES
I. CHRONOPHARMACOKINETICS
It refers to temporal changes in rate processes like absorption and
elimination which may be either cyclical or noncyclical.
aminoglycoside
II. ENZYME INDUCTION
Repeated doses of Carbamazepine induces the enzymes
responsible for its elimination.
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15. III. PROTEIN BINDING
Plasma level- time profiles
of two drugs A and B where
A is 90% protein bound and
B does not bind with plasma
protein.
Ex: Valproic acid.
Fig 6.
Source: Leon Shargel, Applied biopharmaceutics
Pharamacokinetics
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16. PROBLEMS IN QUANTIFYING NON-LINEAR
PHARMACOKINETICS
Estimation of Km and Vm assuming multi compartment would
be more approporiate rather than considering a one
compartment model.
One more problem encounters when a drug is eliminated via
more than one capacity limited processes.[Sedmen et al.] No
problem in Km, when it is in factor of 3.
Drugs which effect the hepatic blood flow in turn effecting the
rate of elimination. The mechanism by which these act are
altering the cardiac outflow.
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17. CONCLUSION
Non linear pharmacokinetics is dose dependent and
does not occur significantly at lower doses of drug.
Probable reasons to occur may be attributed to change
in physiologic system or saturation or protein binding
or enzyme induction.
Though the level of complexity increases when it is
applied more realistic, assuming the process in a
single compartment several pharmacokinetic
parameters are estimated concerned.
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18. REFERENCES
G. Levy. Pharmacokinetics of salicylate elimination in man. J.
Pharm. Sci. 54:959 (1965).
K. Arnold and N. Gerber. The rate of decline of
diphenylhydantoin in human plasma. Clin. Pharmacol. Ther.
11: 121 (1970).
N. Gerber and J. G. Wagner. Explanation of dose-dependent
decline of diphenylhydantoin plasma levels by fitting to the
integrated form of Michaelis-Menten equation. Res. Commun.
Chem. Pathol. Pharmacol. 3: 455 (1972).
L. Martis and R. H. Levy. Bioavailability calculations for
drugs showing simultaneous first -order and capacity-limited
elimination kinetics. J. Pharmacokinet. Biopharm. 1: 283
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(1973) .
19. T. Tsuchiya and G. Levy. Relationship between dose and plateau
levels of drugs eliminated by parallel first-order and capacity-
limited kinetics. J. Pharm. Sci. 61:541(1972).
W. H. Pitlick and R. H. Levy. Time-dependent kinetics: I.
Exponential autoinduction of carbamazepine in monkeys. J. Pharm.
Sci. 66:647 (1977).
BIBILIOGRAPHY
Milo Gibaldi and Donald Perrier. Pharmacokinetics. Second
edition. Volume 15. Marcel Dekker INC. 272-289 (2006).
Leon Shargel, Susanna Wu-Pong and Andrew B.C Yu. Non-linear
Pharmacokinetics. Applied Biopharmaceutics and
Pharmacokinetics. Fifth edition. The McGraw-Hill Companies,
INC. 240-242 (2007)
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